I'll defend PlayStation 3...not just because I work for a Sony-owned development studio.
The PlayStation brand has historically targeted the broadest audience, but as ShiftyBob mentioned, PS3 doesn't have a whole lot of must-have games yet (I'd like to believe Uncharted: Drake's Fortune is one - shameless plug - but it is a teen rated title). Also worth noting: all PS3s can play PSone games and, with the exception of the $399 40GB model, can also play PS2 games...which, technically, gives PS3 access to the largest and most diverse game library.
That said, if you are buying the system primarily for your kids, Nintendo systems are historically hard to beat...and the Wii has the advantage when catering to both kids and non-gaming adults due to its unique control scheme. The Wii also is the least expensive of the three current generation game consoles, so you are probably better off getting the Wii right now. My biggest gripe with the Wii is that it isn't HD...but that doesn't seem to bother the majority of its owners.
Of course, if you really want to save yourself some money, get a PlayStation 2. In addition to their aforementioned library of diverse games, they're small, cheap, and games are still being developed for it (including Guitar Hero III and Rock Band).